Washington (CNN) -- Citing a "deficit of trust" in government by the American people, President Obama's first State of the Union address urged Congress to erode the influence of special interests and work together to confront the nation's most pressing problems.

In the nationally televised speech Wednesday night to a joint session of Congress, Obama sought to reassure Americans angry and nervous about the pace of economic recovery that his government understands the challenges and would act boldly to meet them.

Obama called for a new political climate of "common sense" approaches that invest in the American people without building "a mountain of debt."

"We have to recognize that we face more than a deficit of dollars right now. We face a deficit of trust -- deep and corrosive doubts about how Washington works that have been growing for years," Obama said.

Key areas where Obama wants to build that trust include: the economy, education, energy, health care and national security.

"He outlined a road map that, if followed with bipartisan support in Congress, can reduce our deficit, rebuild our economy and create a new foundation of prosperity for American families and businesses," said Sen. Tom Harkin, D-Iowa.

"It was a serious speech -- reached out to Republicans," said Rep. Steny Hoyer, D-Maryland, the House majority leader.

Republicans, however, were skeptical of Obama's ability to change the partisan atmosphere in Washington.

"Real bipartisanship requires more than just lip service; it demands both sides coming together in a real and meaningful way. It's time for the administration to abandon this big-government agenda and start working in a meaningful way with Republicans to find common-sense solutions to move the country forward," said Sen. Orrin Hatch, R-Utah.

"I would have liked to have seen him emphasize reaching out to the other side of the aisle and bringing us together," said Sen. George Voinovich, R-Ohio.

Analysts, too, were mixed in their reactions to what Obama had to say Wednesday night.

CNN political contributor John Avlon said Obama was targeting independents with his remarks, but questioned his success.

"They still hear The Who's 'Won't Get Fooled Again' in the back of their minds," Avlon said.

Democratic strategist James Carville said Obama made progress. "He picked up a first down tonight," Carville said.

And a post-speech opinion poll shows a divided public.

A CNN/Opinion Research Corp. survey indicated that 48 percent of speech watchers had a very positive reaction, with three in 10 saying they had a somewhat positive response and 21 percent with a negative response.

The 48 percent who indicated they had a very positive response is down 20 points from the 68 percent of speech watchers who felt the same way a year ago about the president's February 24 primetime address to a joint session of Congress.

"Wednesday night's State of the Union audience is more Democratic than the nation as a whole, but speech-watchers were less Democratic this year than they were last year," said Keating Holland, CNN polling director. "That may be one reason why the number who gave his speech a 'very positive' rating is lower this year. But part of the reason also may be that speech-watchers didn't necessarily hear a new agenda and aren't confident that the president can improve health care or lower the deficit."